Question: Simplify the following expression: $r = \dfrac{-36y + 96}{96}$ You can assume $y \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-36y + 96 = - (2\cdot2\cdot3\cdot3 \cdot y) + (2\cdot2\cdot2\cdot2\cdot2\cdot3)$ The denominator can be factored: $96 = (2\cdot2\cdot2\cdot2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $r = \dfrac{(12)(-3y + 8)}{(12)(8)}$ Dividing both the numerator and denominator by $12$ gives: $r = \dfrac{-3y + 8}{8}$